My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
How many different symmetrical shapes can you make by shading triangles or squares?
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
A few extra challenges set by some young NRICH members.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
You need to find the values of the stars before you can apply normal Sudoku rules.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Use the differences to find the solution to this Sudoku.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
A challenging activity focusing on finding all possible ways of stacking rods.
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?